90% of fouling is caused by I'll fitting bullets or driving them to fast
Clean your gun well before switching to lead. Try some out. If you get leading get your throat measured and get appropriate sized bulled.
I am assuming they are pre-lubed.
A difference of opinion here!
I say 90% of lead build up in the bore is due to a microscopically rough bore.
With the naked eye, you can't tell if your barrel is smooth or rough.
I have shot cast bullets in the five different 44 magnum revolvers I have owned and shot extensively, plus two Marlin rifles in 44 magnum. One Ruger got bad build up of lead while another same model of Ruger Blackhawk would never collect a bit of lead and neither did the Marlin rifles. The other three revolvers, two S&W and another Blackhawk, were some where in between.
One time Ruger had a pamphlet out on this subject and all they talked about was a smooth or rough bore. They gave a few methods of polishing the bore, such as a super fine abrasive, like a household polisher, but stated a few hundred jacketed bullets through the bore usually polished them.
Some lead collecting is not a serious problem. Shooting five jacketed after fifty lead bullets will likely keep it cleaned forever.
I know, the CURRENT popular opinion is the bullet has to be the right size. But those bullets obturate to fit the bore. Also, if size was so important, why wouldn't a major supplier of cast bullets, such as The Bullet Barn, offer two or three sizes of a popular calibre, like 357 or 44? And why wouldn't an extremely popular mold, like the Keith 429421 be made in size variations?
OP, you say you have 300 grain bullets. Not my choice, but just load them up and shoot away.
There are far more important things in this world to worry about, than whether or not there is some lead collecting in your gun bore.